We are justified by true living faith.
True living faith requires belief in certain dogmas (
de fide) (this would include among other things a recognition of the need to repent of sin by the power of the Cross).
Failure to hold required belief or to repent of sin is a sign of a lack of true and living faith.
The only difference between our beliefs would be what constitutes doctrines
de fide and thus what is to be required in order to have the faith by which we are justified. As you mentioned, the Marian doctrines are
de fide for Roman Catholics. Anglicans would stick to a smaller number of essential beliefs.
What is in the creeds would be considered necessary to be believed. Explications from the ecumenical councils are similarly held of high importance. The writings of the Fathers and the formularies provide further explication of these doctrines. All are held to be under the final authority of Holy Scripture as God's revealed World, containing all things necessary to salvation.
To phrase the point of losing justification/salvation by "works" here is a hypothetical.
I am a believer. I am baptised. I am saved. I commit adultery and reject Biblical and Church teaching that this is sinful, and therefore never repent of this act. Am I still justified?
Can I at that point truly claim to believe? Do I have faith. Faith is judged by its fruit (works) and my works show that my faith is lacking, even if it was sufficient at one point, because now for whatever reason (viewing Biblical/Church teaching as archaic and so far apart from social mores that they can simply be ignored is typical in these cases, at least among Canadian Anglicans) I am placing myself in God's seat of judgement in order to say what is and isn't acceptable.
At any rate, I've always appreciated
this definition of Anglo-Catholicism (because contrary to what many people today believe, Anglo-Catholicism is more than just stealing Roman ritual) and in the scenario I've described, I would be violating the high view of the Atonement if I were to ignore the role of confession and repentance that comes with exploring works as the fruits of our faith.